Problem: The following line passes through point $(1, 3)$ : $y = -\dfrac{6}{7} x + b$ What is the value of the $y$ -intercept $b$ ?
Explanation: Substituting $(1, 3)$ into the equation gives: $3 = -\dfrac{6}{7} \cdot 1 + b$ $3 = -\dfrac{6}{7} + b$ $b = 3 + \dfrac{6}{7}$ $b = \dfrac{27}{7}$ Plugging in $\dfrac{27}{7}$ for $b$, we get $y = -\dfrac{6}{7} x + \dfrac{27}{7}$. ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ ${1}$ ${2}$ ${3}$ ${4}$ ${5}$ ${6}$ ${7}$ ${8}$ ${9}$ ${10}$ ${\llap{-}2}$ ${\llap{-}3}$ ${\llap{-}4}$ ${\llap{-}5}$ ${\llap{-}6}$ ${\llap{-}7}$ ${\llap{-}8}$ ${\llap{-}9}$ ${\llap{-}10}$ $(1, 3)$